Question

Integrate the function: x logx

Answer 1

Let I = ∫xlog x dx

Taking log x as first function and x as second function and integrating by parts, we obtain

I = log x∫x dx - ∫{(\(\frac {d}{dx} log\ x\))∫x dx} dx

I = log x . \(\frac {x^2}{2}\) - ∫\(\frac 1x\) . \(\frac {x^2}{2}\) dx

I = \(\frac {x^2log\ x}{2}\) - ∫\(\frac x2\) dx

I = \(\frac {x^2log\ x}{2}\) - \(\frac {x^2}{4}\) + C